Answer to Question #269102 in Classical Mechanics for joseph

Question

1. Consider an 8-m-long, 8-m-wide, and 2-m-high aboveground swimming pool that is filled with water to the rim.

(a) Determine the hydrostatic force on each wall and the distance of the line of action of this force from the ground.

(b) If the height of the walls of the pool is doubled and the pool is filled, will the hydrostatic force on each wall double or quadruple? Why?

2. Consider a heavy car submerged in water in a lake with a flat bottom. The driver's side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10 m below the water surface. Determine the net force acting on the door (normal to its surface) and the location of the pressure center if (a) the car is well-sealed, and it contains air at atmospheric pressure and (b) the car is filled with water.

Answer 1

1.

a)

$F=pS=\rho g h(hl)=\rho gh^2l=320~kN,$

$d=\frac h2=1~m.$

b)

$F\sim h^2,$

the hydrostatic force is quadruple if the height of the walls is doubled.

2.

$p=p_0+\rho g(h+\frac b2)=205~kPa,$

$F=pS=pab=203~kN.$

When the car is filled with air or it is filled with water, in both the cases pressure centre will lie at the centre of the door.